Now, I should mention that I am not a mathematician or physicist in any way, shape or form (otherwise, I wouldn't still be taking a basic Linear Algebra course five months short of my 40th birthday). I know just enough to realize that what I'm about to ask is absolutely nuts; still, the idea just interests me enough to ask about it.

I was reading a bit in a textbook on elementary Euclidean n-space vector, drifting into the hypnogogic state often induced by the prose of such works, when one of the comments it made brought me to attention:

Anton and Rorres wrote:[A]n order n-tuple can be viewed as either a "generalized point" or a "generalized vector" - the distinction is mathematically unimportant. [emphasis added]

For some reason, it struck me that this sounded familiar - namely, it vaguely resembled the descriptions of wave-particle duality in some popular (in the sense of "for the non-mathematical layman") books about modern physics ('modern' being 'after 1900'). It seemed to me also to have a vague homology to the uncertainty principle, though I couldn't quite put a finger on how.

Now, before anyone says anything, I already know that this isn't even vaguely right. I've briefly read up on these subjects (on Wikipedia and such-like, but even so, better than what I knew already) and could readily see that I'm being silly - the mathematics involved in those two phenomena are not only vastly different, they are not especially related to each other. Still, the idea seems to be sticking in my mind at the moment, and I could use to have someone tear it apart specifically - or at the very least, to air the idea for others to laugh at. Think if it as me lancing a mental boil, if you will.